# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Still on LOP's (mea culpa)
From: Michael Wescott
Date: 2002 Apr 26, 10:26 -0400

```>> Given that each observation comes from the same Gaussian distribution
>> the joint probability density is proportional to
>>
>>        exp( -(d1**2 + d2**2 + d3**2 ... ))
>>
>> where dn is the distance from a point to LOP number n. So it's
>> a matter of minimizing d1**2 + d2**2 + d3**2 ...  to get maximum
>> joint prob density or MPP. In other words it's a least squares problem.

> Now I am getting confused anew. If the sigma is the same for each LOP,
> then how can the expression below weight dN differently from dM. All
> the d's are squared inside the exp(). So in a 3-LOP case, how could the
> center be anything but the center of the inscribed circle (i.e. all d
> the same value)?

By geometry. If you move the candidate point for MPP almost parallel to
side N and side P, dM can get smaller faster than dN and dP get bigger.
It depends on their mutual orientation.

--
Mike Wescott
Wescott_Mike{at}EMC.COM

```
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